Why do Christians believe they will rise again?
The really simple answer is: Because Jesus Christ said so, and we believe everything that He said. The longer answer is somewhat similar and comes from the bible (if you want to know why we believe the bible, go to "What is the bible?"). There are many references to Jesus returning for His followers, living or already passed away.
For the Lord himself (that's Jesus Christ) will come down from heaven with a commanding shout, with the voice of the archangel, and with the trumpet call of God. First, the believers who have died will rise from their graves. Then, together with them, we who are still alive and remain on the earth will be caught up in the clouds to meet the Lord in the air. Then we will be with the Lord forever. So encourage each other with these words. (1 Thessalonians 4:16-18 NLT)
In this passage we can clearly see that God already has plans for those who follow Jesus Christ in this life. Even if we have died before He comes back, part of the reason for His return is to fetch the believers who have died AND those still alive, to go to be with God in His kingdom, for ever. That seems clear enough to me!
In this passage from Matthew's Gospel, Jesus Himself is telling His disciples what will happen in the future:
And then at last, the sign that the Son of Man (Jesus) is coming will appear in the heavens, and there will be deep mourning among all the peoples of the earth. And they will see the Son of Man coming on the clouds of heaven with power and great glory. And he will send out his angels with the mighty blast of a trumpet, and they will gather his chosen ones from all over the world—from the farthest ends of the earth and heaven. (Matthew 24:30-31 NLT)
There is a great deal more - especially in the New Testament, as you would expect, but also in the Old - predicted even before Jesus came to Earth as a man. There is very good reason to believe that those who accept Jesus Christ as their leader (Lord and Saviour) in this life, will meet Him again in the next. Even if that were not true, following Jesus in this life is a very much better path than trying to navigate life on our own. As Jesus said about those who follow Him: "... My purpose is to give them a rich and satisfying life". (John 10:10)